Question 5.11: Effect of Friction on Fluid Temperature and Head Loss Show t...
Effect of Friction on Fluid Temperature and Head Loss
Show that during steady and incompressible flow of a fluid in an adiabatic flow section (a) the temperature remains constant and there is no head loss when friction is ignored and (b) the temperature increases and some head loss occurs when frictional effects are considered. Discuss if it is possible for the fluid temperature to decrease during such flow (Fig. 5–57).
Steady and incompressible flow through an adiabatic section is considered. The effects of friction on the temperature and the heat loss are to be determined.
Assumptions 1 The flow is steady and incompressible. 2 The flow section is adiabatic and thus there is no heat transfer, q_{net in} = 0.
Analysis The density of a fluid remains constant during incompressible flow and the entropy change is
\Delta s = c_v \ln \frac{T_2}{T_1}
This relation represents the entropy change of the fluid per unit mass as it flows through the flow section from state 1 at the inlet to state 2 at the outlet. Entropy change is caused by two effects: (1) heat transfer and (2) irreversibilities. Therefore, in the absence of heat transfer, entropy change is due to irreversibilities only, whose effect is always to increase entropy.
(a) The entropy change of the fluid in an adiabatic flow section (q_{net in} = 0) is zero when the process does not involve any irreversibilities such as friction and swirling turbulent eddies, and thus for adiabatic reversible flow we have
Temperature change: \Delta s = c_v \ln \frac{T_2}{T_1} = 0 → T_2=T_1
Mechanical energy loss: e_{mech loss, piping} = u_2 – u_1 – q_{net in} = c_v (T_2 – T_1) – q_{net in} = 0 – 0 = 0
Head loss: h_L = e_{mech loss, piping} / g =0
Thus we conclude that when heat transfer and frictional effects are negligible, (1) the temperature of the fluid remains constant, (2) no mechanical energy is converted to thermal energy, and (3) there is no irreversible head loss.
(b) When irreversibilities such as friction are taken into account, the entropy change is positive and thus we have:
Temperature change: \Delta s = c_v \ln \frac{T_2}{T_1} > 0 → T_2 >T_1
Mechanical energy loss: e_{mech loss, piping} = u_2 − u_1 − q_{net in} = c_v(T_2 − T_1) > 0
Head loss: h_L = e_{mech loss, piping}/g > 0
Thus we conclude that when the flow is adiabatic and irreversible, (1) the temperature of the fluid increases, (2) some mechanical energy is converted to thermal energy, and (3) some irreversible head loss occurs.
Discussion It is impossible for the fluid temperature to decrease during steady, incompressible, adiabatic flow since this would require the entropy of an adiabatic system to decrease, which would be a violation of the second law of thermodynamics.